# | Date | Topic |
---|---|---|
1 | Wednesday, January 4 | Course Information and Tentative Outline. |
2 | Wednesday, January 4 | AG Table of Contents and Preface. |
3 | Wednesday, January 4 | AG Bibliography and Index. |
4 | Wednesday, January 4 | AG Chapter 1: Numerical Algorithms & Errors. |
5 | Friday, January 6 | AG Chapter 2: Roundoff Errors. |
6 | Monday, January 9 | AG Chapter 10: Polynomial Interpolation. |
7 | Monday, January 16 | Linear algebra facts particularly useful to interpolation. More details of numerical linear algebra can be found in Heath chapter 2. |
8 | Monday, January 16 | Review of Linear Algebra: AG Chapter 4: Linear Systems Introduction. CPSC 302 students already have this chapter. |
9 | Wednesday, January 18 | AG Chapter 11: Piecewise Polynomial Interpolation. |
10 | Friday, February 3 | AG Chapter 12: Best Approximation. |
11 | Wednesday, February 22 | AG Chapter 13: Fourier & Wavelet Transforms. |
12 | Monday February 27 | AG Chapter 14: Numerical Differentiation. |
13 | Wednesday March 8 | AG Chapter 16: Initial Value Ordinary Differential Equations |
14 | Wednesday March 8 | AG Chapter 15: Numerical Integration. |
Collaboration Policy:
You may collaborate with other students in the class on homework questions prior to writing up the version that you will submit. This collaboration may include pseudo-code solutions to programming components. Once you begin writing the version that you will submit, you may no longer collaborate on that question, either by discussing the solution with other students, showing your solution to other students, or looking at the solutions written by other students. You may never share executable code (including Matlab m-files) for homework questions.
You may seek help from the course instructor or TA at any time while preparing your homework solutions. You may not receive help from any other person.
If you feel that you have broken this collaboration policy, you may cite in your homework solution the name of the person from whom you received help, and your grade will be suitably adjusted to take this collaboration into account. If you break this collaboration policy and fail to cite your collaborator, you will be charged with plagarism as outlined in the university calendar. If you have any questions, please contact the instructor.
More information is available from (among other sources):
Homework Submission Policy:
Homeworks:
# | Topic | Assigned | Due Date | Assignment | Other Assignment Files | Solution | Other Solution Files | Omitted |
---|
Intended Audience: Undergraduates in
Prerequisites:
Instructor: Ian Mitchell
|
TA: Kangkang Yin
|
TA: Jelena Sirovljevic
|
Course Communication:
Lectures: 11:00 - 12:00, Monday / Wednesday / Friday, Dempster 110
Grades: Your final grade will be based on a combination of:
Textbook:
Other References:
# | Date | Topic | Links | Required Readings | Optional Readings |
---|---|---|---|---|---|
1 | Jan 4 | Course Syllabus and administration. Collaboration guidelines. Professor introduction. | Ian Mitchell's research slides. Ian Mitchell's homepage. | None. | H Preface; AG Preface; BF Preface |
2 | Jan 6 | Introduction to Scientific Computing. Sources (Types) of Error. Problem sensitivity. | Scientific Computing overview slides. Nick Trefethen's essay on the definition of numerical analysis. | H 1.1-1.2; AG 1.1 | H 1.4-1.5 |
3 | Jan 9 | Algorithm Stability. Measures of Error: Absolute & Relative. Methods of Analyzing Error: Forward and Backward. | None. | H 1.2; AG 1.2 | AG 1.3; BF 1.3 |
4 | Jan 11 | Floating Point: Properties & Arithmetic. Sources (Types) of Error during Computation: Truncation and Rounding. | An interview William Kahan, "father" of IEEE floating point. Kahan's lecture notes on IEEE 754 | H 1.3; AG 2 | BF 1.2 |
5 | Jan 13 | Interpolation: Background, Problem Formulation, Monomial Basis. | An example of polynomial interpolation in Matlab: interpolateSine.m | H 7.0-7.3.1; AG 10.0-10.1 | BF 3.0 |
6 | Jan 16 | Lagrange Basis. | None. | H 7.3.2; AG 10.2 | BF 3.1 |
7 | Jan 18 | Newton Basis & Divided Differences. | None. | H 7.3.3; AG 10.3 | BF 3.2 |
8 | Jan 20 | Interpolation Error. | None. | H 7.3.5; AG 10.4 | AG 10.7 |
9 | Jan 23 | Osculating Interpolation. | None. | AG 10.5 | BF 3.3 |
10 | Jan 25 | Piecewise Polynomial Interpolation. | None. | H 7.4.1; AG 11.0-11.1 | BF 3.4 |
11 | Jan 27 | Cubic Splines. Piecewise Hermite. | Example and the code piecewiseCubic.m | H 7.4.2; AG 11.2 | BF 3.4 |
12 | Jan 30 | Polynomial Interpolant Review. | None. | None. | H 7.5-7.6; AG 11.7; BF 3.6 |
Feb 1 | Midterm 1. | ||||
13 | Feb 3 | B-spines & Parameteric Curves. | None. | H 7.4.3; AG 11.3-11.4 | BF 3.5 |
14 | Feb 6 | Best Approximation. Problem Formulation. | None. | AG 12.0 | None. |
15 | Feb 8 | Discrete Least Squares Data Fitting. | bestFitNormChoice.m computes the best linear fit under various norms for the data from class. Results | AG 12.1; H 3.1 | H 3.2; BF 8.1 |
16 | Feb 10 | More Discrete Least Squares Data Fitting. | lsExample.m computes least squares regression (best fits) for two model functions from class. Results | H 3.4.1 | H 3.3 (or even H 3) |
Feb 13-17 | Midterm Break. | ||||
17 | Feb 20 | Continuous Least Squares Approximation. | None. | AG 12.2; H 7.3.5 | BF 8.2 |
18 | Feb 22 | Orthogonal Polynomials. | lsContinuous.m computes continuous least squares best fit polynomial to f(x) = 4 x^3. | AG 12.3; H 7.3.4 | AG 12.4; BF 8.2 |
19 | Feb 24 | Gram-Schmidt Orthogonalization. Chebyshev Approximation. Fourier Transform. | Gram-Schmidt Algorithm Slide | AG 12.5, 13.1; H 3.5.3 | AG 12.7; BF 8.3 |
20 | Feb 27 | Discrete Fourier Transform. Wavelets mentioned. | dft.m computes the best fit trigonometric approximant or discrete Fourier Transform. | AG 13.2, 13.4; H 12.1 | H 12.3; BF 8.5 |
21 | March 1 | Complex Exponential Basis of the Fast Fourier Transform. Review of Interpolation and Best Approximation. | None. | AG 13.3 (ha!); H 12.2 | AG 13.6; H 12.4-12.6; BF 8.6 |
22 | March 3 | Numerical Differentiation. Symbolic & Automatic Differentiation. Taylor Series Methods. | None. | AG 14.0 - 14.1; H 8.6 | BF 4.1 |
22 | March 3 | Interpolate & Differentiate. Lagrange Basis Formulae. | None. | AG 14.2; H 8.6 | None |
March 8 | Midterm 2. | ||||
24 | March 10 | Errors in Numerical Differentiation. Richardson Extrapolation. | None. | AG 14.4, 14.6; H 8.7 | BF 4.2 |
25 | March 13 | Ordinary Differential Equations Introduction. | None. | AG 16.0; H 9.1 | BF 5.1 |
26 | March 15 | High order ODE Reformulation. Lipschitz continuity. | None. | H 9.1 | BF 5.9 |
27 | March 17 | ODE existence, uniqueness & conditioning. ODE Basic Methods: Forward Euler. | Example codes: stiff.m, circle.m, and matlabFailure.m. For more information, see the ODE links below. | AG 16.1; H 9.2-9.3.1 | BF 5.2 |
28 | March 20 | Integrator Error Analysis. Backward Euler, Implicit Trapezoidal & Explicit Midpoint. | None. | H 9.3.3 | None. |
29 | March 22 | Higher Order Accuracy: Runge-Kutta Methods. | None. | AG 16.2; H 9.3.6 | AG 16.4; H 9.3.5, 9.3.7-9.3.9; BF 5.4 |
30 | March 24 | Error Estimation and Control. | None. | AG 16.3 | BF 5.5 |
31 | March 27 | Stiffness & Stability | stiff.m demonstrates a stiff system. | H 9.3.2, 9.3.4 | AG 16.7; H 9.4-9.5; BF 5.10-5.11 |
32 | March 29 | Introduction to Numerical Integration. Basic Quadrature. | Examples | AG 15.0 - 15.1; H 8.1-8.3.2 | BF 4.3 |
33 | March 31 | Composite Quadrature | None. | AG 15.2; H 8.3.5 | BF 4.4 |
34 | April 3 | Review Basic & Composite Quadrature. Composite Quadrature Example. | None. | None. | None. |
35 | April 5 | Gaussian Quadrature. | None. | AG 15.3; H 8.3.3-8.3.4 | BF 4.7 |
36 | April 7 | Adaptive Quadrature and (Brief) Review. | None. | AG 15.4; H 8.3.6 | AG 15.5-15.8; H 8.4, 8.8-8.9; BF 4.6 |
April 12 | Final Exam: April 12, 3:30pm, DMP 110 (the regular classroom) |